Answer:
8
Step-by-step explanation:
We observe that the logarithm bases are ...
5√5 = √125 . . . . . 125 is the 2nd power of this
2√2 = √8 . . . . . . . 8 is the 2nd power of this; 64 is the 4th power of √8
If we define ...
[tex]p=\sqrt{125}\\q=\sqrt{8}[/tex]
Then our logarithms are ...
[tex]\log_{p}{p^2}=x=2\\\\\log_{q}{q^4}=y=4\\\\xy=2\cdot 4=8[/tex]
The product of x and y is 8.
